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Electromagnetic Induction

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Electrical transformers. Calculate the mutual inductance of two conducting coils ... Mutual Inductance: Transformers. The self-induced voltage in the primary is: ... – PowerPoint PPT presentation

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Title: Electromagnetic Induction

1
Electromagnetic Induction
• Chapter 22

2
Expectations
• After this chapter, students will
• Calculate the EMF resulting from the motion of
conductors in a magnetic field
• Understand the concept of magnetic flux, and
calculate the value of a magnetic flux
• Understand and apply Faradays Law of
electromagnetic induction
• Understand and apply Lenzs Law

3
Expectations
• After this chapter, students will
• Apply Faradays and Lenzs Laws to some
particular devices
• Electric generators
• Electrical transformers
• Calculate the mutual inductance of two conducting
coils
• Calculate the self-inductance of a conducting
coil

4
Motional EMF
• A wire passes through a uniform magnetic field.
The length of the wire, the magnetic field, and
the velocity of the wire are all perpendicular to
one another

5
Motional EMF
• A positive charge in the wire experiences a
magnetic force, directed upward

6
Motional EMF
• A negative charge in the wire experiences the
same magnetic force, but directed downward
• These forces tend to separate the charges.

7
Motional EMF
• The separation of the charges produces an
electric field, E. It exerts an attractive force
on the charges

E
8
Motional EMF
• In the steady state (at equilibrium), the
magnitudes of the magnetic force separating
the charges and the Coulomb force attracting
them are equal.

E
9
Motional EMF
• Rewrite the electric field as a potential
• Substitute this result back into our earlier
equation

E
10
Motional EMF
• Substitute this result back into our earlier
equation

E
11
Motional EMF
• This is called motional EMF. It results from the
constant velocity of the wire through the
magnetic field, B.

E
12
Motional EMF
• Now, our moving wire slides over two other wires,
forming a circuit. A current will flow, and
power is dissipated in the resistive load

13
Motional EMF
• Where does this power come from?
• Consider the magnetic
• force acting on the
• current in the sliding
• wire

14
Motional EMF
• Right-hand rule 1 shows that this force opposes
the motion of the wire. To move the wire at
constant velocity requires an equal and opposite
force.
• That force does work
• The power

15
Motional EMF
• The forces magnitude was calculated as
• Substituting
• which is the same as the
• power dissipated electrically.

16
Motional EMF
• Suppose that, instead of being perpendicular to
the plane of the sliding-wire circuit, the
perpendicular to that plane.
• The perpendicular
• component of B B cos f

17
Motional EMF
• The motional EMF
• Rewrite the velocity
• Substitute

18
Motional EMF
• L Dx is simply the change in the loop area.

19
Motional EMF
• Define a quantity F
• Then
• F is called magnetic
• flux.
• SI units Tm2 Wb (Weber)

20
Magnetic Flux
• Wilhelm Eduard Weber
• 1804 1891
• German physicist and mathematician

21
• In our previous result, we said that the induced
EMF was equal to the time rate of change of
magnetic flux through a conducting loop. This,
rewritten slightly, is called Faradays Law
• Why the minus sign?

22
• 1791 1867
• English physicist
• and mathematician

23
conducting loops (a coil)
• What can change the magnetic flux?
• B could change, in magnitude or direction
• A could change
• f could change (the coil could rotate)

24
Lenzs Law
Law
• Lenzs Law says that the direction of the induced
current is always such as to oppose the change in
magnetic flux that produced it.
that.

25
Lenzs Law
• Heinrich Friedrich Emil Lenz
• 1804 1865
• Russian physicist

26
Lenzs Law
• Lenzs Law says that the direction of the induced
current is always such as to oppose the change in
magnetic flux that produced it.
• What does that mean?
• How can an induced current oppose a change in
magnetic flux?

27
Lenzs Law
• How can an induced current oppose a change in
magnetic flux?
• A changing magnetic flux induces a current.
• The induced current produces a magnetic field.
• The direction of the induced current determines
the direction of the magnetic field it produces.
• The current will flow in the direction (remember
right-hand rule 2) that produces a magnetic
field that works against the original change in
magnetic flux.

28
• A coil rotates with a constant angular speed in a
magnetic field.
• but f changes
• with time

29
• So the flux also changes with time
• Get the time rate of change (a calculus problem)

30
• The maximum voltage occurs when
• What makes the voltage larger?
• more turns in the coil
• a larger coil area
• a stronger magnetic field
• a larger angular speed

31
Back EMF in Electric Motors
• An electric motor also contains a coil rotating
in a magnetic field.
• In accordance with Lenzs Law, it generates a
voltage, called the back EMF, that acts to oppose
its motion.

32
Back EMF in Electric Motors
• Apply Kirchhoffs loop rule

33
Mutual Inductance
• A current in a coil produces a magnetic field.
• If the current changes, the magnetic field
changes.
• Suppose another coil is nearby. Part of the
magnetic field produced by the first coil
occupies the inside of the second coil.

34
Mutual Inductance
• Faradays Law says that the changing magnetic
flux in the second coil produces a voltage in
that coil.
• The net flux in the
• secondary

35
Mutual Inductance
• Convert to an equation, using a constant of
proportionality

36
Mutual Inductance
• The constant of proportionality is called the
mutual inductance

37
Mutual Inductance
• Substitute this into Faradays Law
• SI units of mutual inductance Vs / A henry (H)

38
Mutual Inductance
• Joseph Henry
• 1797 1878
• American physicist

39
Self-Inductance
• Changing current in a primary coil induces a
voltage in a secondary coil.
• Changing current in a coil also induces a voltage
in that same coil.
• This is called self-inductance.

40
Self-Inductance
• The self-induced voltage is calculated from
Faradays Law, just as we did the mutual
inductance.
• The result
• The self-inductance, L, of a coil is also
measured in henries. It is usually just called
the inductance.

41
Mutual Inductance Transformers
• A transformer is two coils wound around a common
iron core.

42
Mutual Inductance Transformers
• The self-induced voltage in the primary is
• Through mutual induction, and EMF appears in the
secondary
• Their ratio

43
Mutual Inductance Transformers
• This transformer equation is normally written
• The principle of energy conservation requires
that the power in both coils be equal (neglecting
heating losses in the core).

44
Inductors and Stored Energy
• When current flows in an inductor, work has been
done to create the magnetic field in the coil.
As long as the current flows, energy is stored in
that field, according to

45
Inductors and Stored Energy
• In general, a volume in which a magnetic field
exists has an energy density (energy per unit
volume) stored in the field